Finite Group Databasebeta

← #14769336

Subgroups — #14769336

Order 2816.

1446 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×C22⋊D11C211yesmaximal, characteristic
2C2×#10622341C211yesmaximal, characteristic
3C2×#10622838C211yesmaximal, characteristic, complemented
4C2×D11×#103C211yesmaximal, characteristic, complemented
5#13071538C211yesmaximal, characteristic
6#13069537C211yesmaximal, characteristic, complemented
7#13069434C211yesmaximal, characteristic, complemented
8#13069047C211yesmaximal, characteristic, complemented
9#13069036C211yesmaximal, characteristic, complemented
10#13068926C211yesmaximal, characteristic, complemented
11#13068920C211yesmaximal, characteristic, complemented
12#13068629C211yesmaximal, characteristic, complemented
13#13068549C211yesmaximal, characteristic, complemented
14#13068448C211yesmaximal, characteristic, complemented
15C11×#1787C211yesmaximal, characteristic, complemented
16C23×Q8×C11C2211yescharacteristic
17C22×Q8×D11C2211yescharacteristic
18Q8×C22⋊D11—24no—
19Q8×C22⋊D11C418yescomplemented
20C2×#66999—21no—
21C2×#66999C2211yescharacteristic
22C2×Q8×Dic11C2211yescharacteristic
23C2×#66997—21no—
24C2×#66997C2211yescharacteristic
25C2×C4×C22⋊D11—21no—
26C2×C4×C22⋊D11C2211yescharacteristic
27C2×#66979C2211yescharacteristic
28C2×#66977—21no—
29C2×#66977C2211yescharacteristic
30C22×#4318C2211yescharacteristic
31C22×C8×D11C2211yescharacteristic
32C2×C4⋊C4×D11C2211yescharacteristic
33C2×C11×#103C2211yescharacteristic
34C2×C11×#103C2211yescharacteristic
35C2×C11×#103C2211yescharacteristic
36C2×C11×#103C2211yescharacteristic
37C2×C11×C22⋊C8C2211yescharacteristic
38C11×#380C2211yescharacteristic
39#10622838—24no—
40C2×#66899C2211yescharacteristic
41C2×#66899C2211yescharacteristic
42C2×#66899C2211yescharacteristic
43C2×#66899C2211yescharacteristic
44C2×(C2×D11)⋊C8C2211yescharacteristic
45C2×#66880C2211yescharacteristic
46C2×#66880C2211yescharacteristic
47C2×#66879C2211yescharacteristic
48C2×Dic11⋊C8C2211yescharacteristic
49#10622600C2211yescharacteristic
50#10622590C2211yescharacteristic
51C4⋊C4×Dic11C2211yescharacteristic
52C2×#66874C2211yescharacteristic
53C2×#66874C2211yescharacteristic
54#10622569—21no—
55#10622557—21no—
56D11×#103—24no—
57#10622341—24no—
58#10622279—21no—
59#10622265—21no—
60#10622189C2211yescharacteristic
61#10622189C2211yescharacteristic
62#10622167C2211yescharacteristic
63#10622167C2211yescharacteristic
64C22×Q8×C11—21no—
65C22×Q8×C11—22no—
66C22×Q8×C11—22no—
67C22×Q8×C11—22no—
68C22×Q8×C11—41no—
69C22×Q8×C11—41no—
70C22×Q8×C11C2×C414yescomplemented
71C22×Q8×C11C2311yescharacteristic
72C22×Q8×C11C2311yescharacteristic
73C23×C4×C11—21no—
74C23×C4×C11C2311yescharacteristic
75C22×C22⋊D11D411yescharacteristic
76C2×Q8×D11—22no—
77C2×Q8×D11—22no—
78C2×Q8×D11—22no—
79C2×Q8×D11—41no—
80C2×Q8×D11—41no—
81C2×Q8×D11C2×C414yes—
82C22×C4×D11—21no—
83C22×C4×D11—21no—
84C22×C4×D11C2311yescharacteristic
85C22×Dic22—21no—
86C22×Dic22C2311yescharacteristic
87C22×C8×C11C2311yescharacteristic
88C22×C8×C11C2311yescharacteristic
89C2×C11×C4⋊C4C2311yescharacteristic
90C2×C11×C4⋊C4C2311yescharacteristic
91C2×C11×C22⋊C4—21no—
92C2×C22⋊Dic11—21no—
93C2×C22⋊Dic11—21no—
94C2×C22⋊Dic11D411yescharacteristic
95#66999—22no—
96#66999—28no—
97#66999C2×C414yes—
98Q8×Dic11—22no—
99Q8×Dic11C2×C414yescomplemented
100#66997—28no—
101#66997—22no—
102#66997C2×C414yescomplemented
103C4×C22⋊D11—28no—
104C4×C22⋊D11C2×C414yes—
105C4×C22⋊D11D414yes—
106C2×(C2×D11)⋊C4—21no—
107C2×(C2×D11)⋊C4—21no—
108C2×(C2×D11)⋊C4D411yescharacteristic
109#66979—22no—
110#66979—41no—
111C2×C4⋊Dic11—21no—
112C2×C4⋊Dic11C2311yescharacteristic
113C2×C4⋊Dic11C2311yescharacteristic
114C2×C4⋊Dic11C2311yescharacteristic
115#66977—22no—
116#66977—28no—
117#66977C2×C414yescomplemented
118C2×Dic11⋊C4—21no—
119C2×Dic11⋊C4—21no—
120C2×Dic11⋊C4—21no—
121C2×Dic11⋊C4—21no—
122C2×Dic11⋊C4—21no—
123C2×Dic11⋊C4D411yescharacteristic
124C2×C4×Dic11—21no—
125C2×C4×Dic11—21no—
126C2×C4×Dic11—21no—
127C2×C4×Dic11C2311yescharacteristic
128C2×#4318—22no—
129C2×#4318—22no—
130C2×#4318—41no—
131C22×C11⋊C8C2311yescharacteristic
132C22×C11⋊C8C2311yescharacteristic
133C2×C8×D11—22no—
134C2×C8×D11—22no—
135C2×C8×D11—41no—
136C4⋊C4×D11—22no—
137C4⋊C4×D11—41no—
138C11×#103—22no—
139C11×#103—22no—
140C11×#103—41no—
141C11×#103—41no—
142C11×C22⋊C8—22no—
143C11×#95—21no—
144#66899—22no—
145#66899—22no—
146#66899—22no—
147#66899D414yescomplemented
148C11⋊#95—21no—
149C11⋊#95—21no—
150C11⋊#95—21no—
151C11⋊#95—21no—
152(C2×D11)⋊C8—22no—
153#66880—22no—
154#66880—41no—
155#66879—22no—
156Dic11⋊C8—22no—
157#66874—22no—
158#66874—41no—
159#22425—111nomaximal, Sylow
160C24×C11C2×D411yescharacteristic
161C23×D11C2×D411yescharacteristic
162C2×Q8×C11—24no—
163C2×Q8×C11—21no—
164C2×Q8×C11—21no—
165C2×Q8×C11—21no—
166C2×Q8×C11—21no—
167C2×Q8×C11—28no—
168C2×Q8×C11—21no—
169C2×Q8×C11—21no—
170C2×Q8×C11—21no—
171C2×Q8×C11—21no—
172C2×Q8×C11—42no—
173C2×Q8×C11—42no—
174C2×Q8×C11—44no—
175C2×Q8×C11—44no—
176C2×Q8×C11—44no—
177C2×Q8×C11C22×C412yes—
178C2×Q8×C11C22×C412yes—
179C2×Q8×C11C2×D412yes—
180C2×Q8×C11#4112yes—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—24no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—42no—
191C22×C4×C11—42no—
192C22×C4×C11C22×C412yes—
193C22×C4×C11C2×D411yescharacteristic
194C22×C4×C11C2×D412yes—
195C22×C4×C11C2411yescharacteristic
196C2×C22⋊D11—22no—
197C2×C22⋊D11—22no—
198C2×C22⋊D11C22⋊C414yes—
199C22×Dic11—21no—
200C22×Dic11—21no—
201C22×Dic11—21no—
202C22×Dic11—21no—
203C22×Dic11C2×D411yescharacteristic
204C22×Dic11C2×D411yescharacteristic
205C22×Dic11C2×D411yescharacteristic
206Q8×D11—28no—
207Q8×D11—44no—
208Q8×D11—44no—
209Q8×D11—44no—
210C2×C4×D11—24no—
211C2×C4×D11—21no—
212C2×C4×D11—21no—
213C2×C4×D11—21no—
214C2×C4×D11—21no—
215C2×C4×D11—42no—
216C2×C4×D11—42no—
217C2×C4×D11—42no—
218C2×C4×D11—42no—
219C2×C4×D11—81no—
220C2×C4×D11C22×C412yes—
221C2×C4×D11C2×D412yes—
222C2×Dic22—24no—
223C2×Dic22—21no—
224C2×Dic22—21no—
225C2×Dic22—21no—
226C2×Dic22—21no—
227C2×Dic22—21no—
228C2×Dic22—42no—
229C2×Dic22—42no—
230C2×Dic22C22×C412yes—
231C2×C8×C11—21no—
232C2×C8×C11—21no—
233C2×C8×C11—21no—
234C2×C8×C11—21no—
235C2×C8×C11—21no—
236C2×C8×C11—21no—
237C11×C4⋊C4—21no—
238C11×C4⋊C4—21no—
239C11×C4⋊C4—21no—
240C11×C4⋊C4—21no—
241C11×C22⋊C4—81no—
242C22⋊Dic11—24no—
243C22⋊Dic11—42no—
244C22⋊Dic11C22⋊C414yes—
245(C2×D11)⋊C4—24no—
246(C2×D11)⋊C4—42no—
247(C2×D11)⋊C4C22⋊C414yes—
248C4⋊Dic11—24no—
249C4⋊Dic11—21no—
250C4⋊Dic11—21no—
251C4⋊Dic11—21no—
252C4⋊Dic11—21no—
253C4⋊Dic11C22×C412yes—
254C4⋊Dic11C2×D412yes—
255Dic11⋊C4—24no—
256Dic11⋊C4—24no—
257Dic11⋊C4—24no—
258Dic11⋊C4—24no—
259Dic11⋊C4—42no—
260Dic11⋊C4C22⋊C414yes—
261C4×Dic11—24no—
262C4×Dic11—42no—
263C4×Dic11—81no—
264C4×Dic11C22×C412yes—
265C4×Dic11C2×D412yes—
266#4318—44no—
267C2×C11⋊C8—21no—
268C2×C11⋊C8—21no—
269C2×C11⋊C8—21no—
270C2×C11⋊C8—21no—
271C2×C11⋊C8—21no—
272C2×C11⋊C8C2×D412yes—
273C8×D11—44no—
274C2×D4×Q8—111no—
275C2×#435—111no—
276C2×#419—111no—
277C22×#103—111no—
278#2352—111no—
279#1981—111no—
280#1960—111no—
281#1894—111no—
282#1892—111no—
283#1873—111no—
284#1872—111no—
285#1805—111no—
286#1787—111no—
287#1787D1111yescharacteristic, complemented
288#1763—111no—
289C23×C11—21no—
290C23×C11—21no—
291C23×C11—21no—
292C23×C11—21no—
293C23×C11—21no—
294C23×C11—21no—
295C23×C11C2×C22⋊C412yes—
296C23×C11C22×D411yescharacteristic
297C22×D11—21no—
298C22×D11—21no—
299C22×D11—21no—
300C22×D11—21no—
301C22×D11C2×C22⋊C412yes—
302C22×D11#13712yes—
303C22×D11#13712yes—
304Q8×C11—22no—
305Q8×C11—22no—
306Q8×C11—22no—
307Q8×C11—22no—
308Q8×C11—22no—
309Q8×C11—48no—
310Q8×C11—41no—
311Q8×C11—41no—
312Q8×C11C4×D414yes—
313C2×C4×C11—22no—
314C2×C4×C11—21no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—21no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—48no—
324C2×C4×C11—41no—
325C2×C4×C11—41no—
326C2×C4×C11—41no—
327C2×C4×C11—41no—
328C2×C4×C11—41no—
329C2×C4×C11—41no—
330C2×C4×C11—41no—
331C2×C4×C11—41no—
332C2×C4×C11C2×C22⋊C412yes—
333C2×C4×C11C23×C411yescharacteristic
334C2×C4×C11C22×D411yescharacteristic
335C2×C4×C11C22×D411yescharacteristic
336C2×C4×C11C2×#4111yescharacteristic
337C2×C4×C11H(5,𝔽2)11yescharacteristic
338C2×C4×C11H(5,𝔽2)11yescharacteristic
339C22⋊D11—28no—
340C2×Dic11—21no—
341C2×Dic11—21no—
342C2×Dic11—21no—
343C2×Dic11—21no—
344C2×Dic11—21no—
345C2×Dic11—21no—
346C2×Dic11—22no—
347C2×Dic11—22no—
348C2×Dic11—22no—
349C2×Dic11—41no—
350C2×Dic11—41no—
351C2×Dic11—41no—
352C2×Dic11—41no—
353C2×Dic11—41no—
354C2×Dic11—41no—
355C2×Dic11—41no—
356C2×Dic11—41no—
357C2×Dic11—41no—
358C2×Dic11C2×C22⋊C412yes—
359C2×Dic11C2×C22⋊C412yes—
360C2×Dic11C2×C22⋊C412yes—
361C4×D11—22no—
362C4×D11—22no—
363C4×D11—22no—
364C4×D11—22no—
365C4×D11—48no—
366C4×D11—84no—
367Dic22—22no—
368Dic22—22no—
369Dic22—48no—
370Dic22—41no—
371Dic22—41no—
372C8×C11—41no—
373C8×C11—41no—
374C11⋊C8—22no—
375C11⋊C8—41no—
376C23×Q8—111no—
377C23×Q8C2×D1111yescharacteristic
378C22×M16—111no—
379C23×C8—111no—
380D4×Q8—118no—
381D4×Q8—224no—
382C2×C4⋊Q8—111no—
383C2×C4⋊Q8—221no—
384C2×C22⋊Q8—111no—
385C2×C22⋊Q8—111no—
386C2×C22⋊Q8—221no—
387C2×C22⋊Q8—221no—
388C2×C4×Q8—111no—
389C2×C4×D4—111no—
390C2×C4×D4—221no—
391C2×#117—111no—
392C22×C4⋊C4—111no—
393#435—224no—
394C2×C4⋊C8—111no—
395#419—224no—
396C2×#103—111no—
397C2×#103—111no—
398C2×#103—111no—
399C2×#103—111no—
400C2×#103—111no—
401C2×#103—111no—
402C2×#103—111no—
403C2×#103—111no—
404C2×#103—224no—
405C2×#103C2×D1111yescharacteristic
406C2×#103C2×D1111yescharacteristic
407C2×#103C2×D1111yescharacteristic
408C2×#103C2×D1111yescharacteristic
409C2×C22⋊C8—111no—
410C2×C22⋊C8C2×D1111yescharacteristic
411C2×#97—111no—
412#388—221no—
413#387—221no—
414#386—221no—
415#382—111no—
416#380—111no—
417#380C2×D1111yescharacteristic
418C4×C4⋊C4—111no—
419C4×C22⋊C4—221no—
420#340—111no—
421#340—111no—
422#340—111no—
423#340—111no—
424C22×C11—22no—
425C22×C11—22no—
426C22×C11—22no—
427C22×C11—41no—
428C22×C11—41no—
429C22×C11—41no—
430C22×C11—41no—
431C22×C11C22×C22⋊C411yescharacteristic
432C22×C11D4211yescharacteristic
433C22×C11#54611yescharacteristic
434C22×C11C2×#13711yescharacteristic
435C22×C11C2×#13711yescharacteristic
436C22×C11#57711yescharacteristic
437C22×C11#57811yescharacteristic
438C2×D11—22no—
439C2×D11—22no—
440C2×D11—22no—
441C2×D11—22no—
442C2×D11—22no—
443C2×D11—22no—
444C2×D11#41914yescomplemented
445C4×C11—22no—
446C4×C11—24no—
447C4×C11—42no—
448C4×C11—81no—
449C4×C11—81no—
450C4×C11C2×C4×D411yescharacteristic
451C4×C11#51811yescharacteristic
452C4×C11D4211yescharacteristic
453C4×C11#54611yescharacteristic
454Dic11—22no—
455Dic11—22no—
456Dic11—22no—
457Dic11—42no—
458Dic11—42no—
459Dic11—42no—
460Dic11—81no—
461C22×Q8—21no—
462C22×Q8—22no—
463C22×Q8—22no—
464C22×Q8—22no—
465C22×Q8—41no—
466C22×Q8—41no—
467C22×Q8—114no—
468C22×Q8—111no—
469C22×Q8—221no—
470C22×Q8—222no—
471C22×Q8—222no—
472C22×Q8—222no—
473C22×Q8—441no—
474C22×Q8—441no—
475C22×Q8C4×D1114yescomplemented
476C22×Q8C22×D1111yescharacteristic
477C22×Q8C22×D1111yescharacteristic
478C22×D4—111no—
479C23×C4—21no—
480C23×C4—111no—
481C23×C4—221no—
482C23×C4—221no—
483C23×C4C22×D1111yescharacteristic
484C2×M16—222no—
485C2×M16—222no—
486C2×M16—441no—
487C22×C8—111no—
488C22×C8—111no—
489C22×C8—222no—
490C22×C8—222no—
491C22×C8—441no—
492C22×C8C22×D1111yescharacteristic
493C22×C8C22×D1111yescharacteristic
494C4⋊Q8—114no—
495C4⋊Q8—222no—
496C4⋊Q8—228no—
497C22⋊Q8—114no—
498C22⋊Q8—114no—
499C22⋊Q8—228no—
500C22⋊Q8—228no—
501C22⋊Q8—222no—
502C22⋊Q8—222no—
503C4×Q8—114no—
504C4×Q8—222no—
505C4×D4—114no—
506C4×D4—114no—
507C4×D4—228no—
508#117—222no—
509#117—441no—
510C2×C4⋊C4—111no—
511C2×C4⋊C4—111no—
512C2×C4⋊C4—111no—
513C2×C4⋊C4—111no—
514C2×C4⋊C4—222no—
515C2×C4⋊C4—221no—
516C2×C4⋊C4—221no—
517C2×C4⋊C4—221no—
518C2×C4⋊C4—221no—
519C2×C4⋊C4—221no—
520C2×C4⋊C4—221no—
521C2×C4⋊C4—441no—
522C2×C4⋊C4C22×D1111yescharacteristic
523C2×C4⋊C4C22×D1111yescharacteristic
524C2×C22⋊C4—21no—
525C2×C22⋊C4—111no—
526C2×C22⋊C4—111no—
527C2×C22⋊C4—221no—
528C2×C22⋊C4—221no—
529C2×C22⋊C4—221no—
530C2×C22⋊C4—221no—
531C2×C42—111no—
532C2×C42—221no—
533C2×C42—221no—
534C2×C42—221no—
535C4⋊C8—222no—
536#103—22no—
537#103—22no—
538#103—41no—
539#103—41no—
540#103—114no—
541#103—222no—
542#103—222no—
543#103—222no—
544#103—222no—
545#103—222no—
546#103—441no—
547#103—441no—
548C22⋊C8—22no—
549C22⋊C8—222no—
550#97—222no—
551#95—21no—
552#95—221no—
553#95—221no—
554#95—221no—
555#95—221no—
556C2×C11—42no—
557C2×C11D4×C22⋊C411yescharacteristic
558C2×C11C2×#41911yescharacteristic
559C2×C11#289811yescharacteristic
560C2×C11#326611yescharacteristic
561C2×C11#327011yescharacteristic
562C2×C11#331211yescharacteristic
563C2×C11#332011yescharacteristic
564D11—24no—
565C24—111no—
566C24D4×D1111yescharacteristic
567C2×Q8—24no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—28no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—42no—
578C2×Q8—42no—
579C2×Q8—44no—
580C2×Q8—44no—
581C2×Q8—44no—
582C2×Q8—112no—
583C2×Q8—224no—
584C2×Q8—221no—
585C2×Q8—228no—
586C2×Q8—221no—
587C2×Q8—221no—
588C2×Q8—221no—
589C2×Q8—221no—
590C2×Q8—442no—
591C2×Q8—442no—
592C2×Q8—444no—
593C2×Q8—444no—
594C2×Q8—444no—
595C2×Q8C2×C4×D1112yes—
596C2×Q8C2×C4×D1112yes—
597C2×Q8D4×D1112yes—
598C2×Q8#434112yes—
599C2×D4—114no—
600C2×D4—222no—
601C2×D4—222no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—24no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—111no—
614C22×C4—111no—
615C22×C4—111no—
616C22×C4—112no—
617C22×C4—112no—
618C22×C4—224no—
619C22×C4—221no—
620C22×C4—221no—
621C22×C4—221no—
622C22×C4—221no—
623C22×C4—221no—
624C22×C4—221no—
625C22×C4—221no—
626C22×C4—221no—
627C22×C4—442no—
628C22×C4—442no—
629C22×C4—442no—
630C22×C4—442no—
631C22×C4—881no—
632C22×C4C2×C4×D1112yes—
633C22×C4D4×D1111yescharacteristic
634C22×C4D4×D1112yes—
635C22×C4C23×D1111yescharacteristic
636M16—444no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—112no—
644C2×C8—221no—
645C2×C8—221no—
646C2×C8—221no—
647C2×C8—221no—
648C2×C8—221no—
649C2×C8—444no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—114no—
655C4⋊C4—112no—
656C4⋊C4—112no—
657C4⋊C4—224no—
658C4⋊C4—224no—
659C4⋊C4—224no—
660C4⋊C4—224no—
661C4⋊C4—224no—
662C4⋊C4—221no—
663C4⋊C4—221no—
664C4⋊C4—221no—
665C4⋊C4—221no—
666C4⋊C4—442no—
667C22⋊C4—81no—
668C22⋊C4—114no—
669C22⋊C4—114no—
670C22⋊C4—224no—
671C22⋊C4—224no—
672C22⋊C4—442no—
673C22⋊C4—442no—
674C42—112no—
675C42—112no—
676C42—224no—
677C42—442no—
678C42—881no—
679C11#2242511yescharacteristic, complemented, Sylow
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—112no—
687C23—112no—
688C23—112no—
689C23—221no—
690C23—221no—
691C23—221no—
692C23—221no—
693C23C22⋊C4×D1112yes—
694C23C2×D4×D1111yescharacteristic
695Q8—22no—
696Q8—22no—
697Q8—22no—
698Q8—22no—
699Q8—22no—
700Q8—48no—
701Q8—41no—
702Q8—41no—
703Q8—222no—
704Q8—222no—
705Q8—448no—
706Q8—441no—
707Q8—441no—
708Q8(C22⋊D11)⋊C414yes—
709D4—228no—
710C2×C4—22no—
711C2×C4—21no—
712C2×C4—22no—
713C2×C4—21no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—48no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—112no—
730C2×C4—112no—
731C2×C4—112no—
732C2×C4—221no—
733C2×C4—221no—
734C2×C4—221no—
735C2×C4—221no—
736C2×C4—221no—
737C2×C4—221no—
738C2×C4—222no—
739C2×C4—222no—
740C2×C4—222no—
741C2×C4—222no—
742C2×C4—222no—
743C2×C4—222no—
744C2×C4—222no—
745C2×C4—448no—
746C2×C4—441no—
747C2×C4—441no—
748C2×C4—441no—
749C2×C4—441no—
750C2×C4—441no—
751C2×C4—441no—
752C2×C4—441no—
753C2×C4—441no—
754C2×C4—441no—
755C2×C4—884no—
756C2×C4C22⋊C4×D1112yes—
757C2×C4C22×C4×D1111yescharacteristic
758C2×C4C2×D4×D1111yescharacteristic
759C2×C4C2×D4×D1111yescharacteristic
760C2×C4C2×#434111yescharacteristic
761C2×C4#6703711yescharacteristic
762C2×C4#6703711yescharacteristic
763C8—41no—
764C8—41no—
765C8—222no—
766C8—441no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—114no—
775C22—222no—
776C22—222no—
777C22—222no—
778C22—222no—
779C22—222no—
780C22—222no—
781C22C2×C22⋊C4×D1111yescharacteristic
782C22#1062312111yescharacteristic
783C22#1062312211yescharacteristic
784C22#1062329311yescharacteristic
785C22#1062329711yescharacteristic
786C22D11×#13711yescharacteristic
787C22D11×#13711yescharacteristic
788C4—22no—
789C4—24no—
790C4—42no—
791C4—81no—
792C4—81no—
793C4—222no—
794C4—222no—
795C4—222no—
796C4—442no—
797C4—442no—
798C4—442no—
799C4—881no—
800C4C2×(C22⋊D11)⋊C411yescharacteristic
801C4#1062301711yescharacteristic
802C4#1062312111yescharacteristic
803C4#1062312211yescharacteristic
804C2—42no—
805C2—224no—
806C2#1307143211yescharacteristic
807C2D11×#41911yescharacteristic
808C2#1307714411yescharacteristic
809C2#1308012911yescharacteristic
810C2#1308018911yescharacteristic
811C2#1308066011yescharacteristic
812C2#1308078011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1787C2
socleC23×C11C22×D4
prime radicalC22×C22⋊D11D4
cosocleC22×C4×C11C24
hypercenter#1787D11
hypocenterC11#22425
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1787

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C2×#10622838C2semidirect
4. C2×D11×#103C2semidirect
6. #13069537C2semidirect
7. #13069434C2semidirect
8. #13069047C2semidirect
9. #13069036C2semidirect
10. #13068926C2semidirect
11. #13068920C2semidirect
12. #13068629C2semidirect
13. #13068549C2semidirect
14. #13068448C2semidirect
15. C11×#1787C2semidirect
19. Q8×C22⋊D11C4semidirect
70. C22×Q8×C11C2×C4semidirect
99. Q8×Dic11C2×C4semidirect
102. #66997C2×C4semidirect
117. #66977C2×C4semidirect
147. #66899D4semidirect
287. #1787D11semidirect
444. C2×D11#419semidirect
475. C22×Q8C4×D11semidirect
679. C11#22425semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×Q8×C22⋊D112
C2×#106223412
C2×#106228382
C2×D11×#1032
#130715382
#130695372
#130694342
#130690472
#130690362
#130689262
#130689202
#130686292
#130685492
#130684482
C11×#17872
#2242511